Question: Multiply the following complex numbers, marked as blue dots on the graph: $[2(\cos(\frac{1}{2}\pi) + i \sin(\frac{1}{2}\pi))] \cdot [3(\cos(\frac{3}{4}\pi) + i \sin(\frac{3}{4}\pi))]$ (Your current answer will be plotted in orange.)
Explanation: Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $2(\cos(\frac{1}{2}\pi) + i \sin(\frac{1}{2}\pi))$ ) has angle $\frac{1}{2}\pi$ and radius $2$ The second number ( $3(\cos(\frac{3}{4}\pi) + i \sin(\frac{3}{4}\pi))$ ) has angle $\frac{3}{4}\pi$ and radius $3$ The radius of the result will be $2 \cdot 3$ , which is $6$ The angle of the result is $\frac{1}{2}\pi + \frac{3}{4}\pi = \frac{5}{4}\pi$ The radius of the result is $6$ and the angle of the result is $\frac{5}{4}\pi$.